Question

proove..

sin3x = 3sinx - 4 sin³x

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Answer 1

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Question-; Proove sin3x = 3sinx - 4 sin³x.

Solution-;

Taking LHS

$sin3x = \sin(2x + x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: =sin2xcosx + cos2xsinx \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2sinxcosxcosx + (1 - 2sin {}^{2} x)sinx \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2sinx(1 - sin {}^{2} x) + sinx - 2sin {}^{3}x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2sinx - 2sin {}^{3} x + sinx - 2sin {}^{3} x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 3sinx - 4sin {}^{3} x \\ \\ \\ \\ hence \: prooved$
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